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# Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y >

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Is x^4 + y^4 > z^4 (1) X^2 + y^2 > z^2 (2) X + Y > [#permalink]  20 Mar 2008, 10:19
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Is x^4 + y^4 > z^4

(1) X^2 + y^2 > z^2
(2) X + Y > Z
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Re: DS : Is x4 + y4 > z4 [#permalink]  20 Mar 2008, 10:35
maverick101 wrote:
Is x^4 + y^4 > z^4

(1) X^2 + y^2 > z^2
(2) X + Y > Z

E.

1 & 2:
if x = y = 0.8 and z = 0.9 ---- yes.
if x = y = 0.7 and z = 0.9 ------- no.
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Re: DS : Is x4 + y4 > z4 [#permalink]  20 Mar 2008, 10:38
E

Is x^4 + y^4 > z^4

(1) x^2 + y^2 > z^2

(2) x + y > z

It is obviously that x=10000, y=10000, z=1 satisfies both conditions and answer is "true".
So, I will try to construct example that satisfies both condition but answer is "false"
1. let x=y and z=1 for simplicity.
2. we need x<1 because x^n will decrease when the power increases.
consider the fist condition: 2*x^2>1 --> x>\sqrt{0.5} \approx 0.7
3. try x=0.8 (it satisfies both conditions): 2*0.8^4 = 2*0.64^2 < 2*0.7^2 < 2*0.49 < 1 bingo!

Here, I've tried to clarify my logic (for myself also ) when I construct examples.....just exercise
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Re: DS : Is x4 + y4 > z4   [#permalink] 20 Mar 2008, 10:38
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